function [f,D] = fnewt(x,a) % Function used by the N-variable Newton's method % Inputs % x State vector [x y z] % a Parameters [r sigma b] % Outputs % f Lorenz model r.h.s. [dx/dt dy/dt dz/dt] % D Jacobian matrix, D(i,j) = df(j)/dx(i) % Evaluate f(i) f(1) = a(2)*(x(2)-x(1)); f(2) = a(1)*x(1)-x(2)-x(1)*x(3); f(3) = x(1)*x(2)-a(3)*x(3); % Evaluate D(i,j) D(1,1) = -a(2); % df(1)/dx(1) D(1,2) = a(1)-x(3); % df(2)/dx(1) D(1,3) = x(2); % df(3)/dx(1) D(2,1) = a(2); % df(1)/dx(2) D(2,2) = -1; % df(2)/dx(2) D(2,3) = x(1); % df(3)/dx(2) D(3,1) = 0; % df(1)/dx(3) D(3,2) = -x(1); % df(2)/dx(3) D(3,3) = -a(3); % df(3)/dx(3) return;